MOSES: Model for Studying the Economy of Sweden. Gunnar Bårdseny, Ard den Reijerz, Patrik Jonassonxand Ragnar Nymoen¶ January 2012 Abstract MOSES is an aggregate econometric model for Sweden, estimated on quarterly data, and intended for policy simulations and short-term forecasting. After a presen- tation of qualitative model properties, the econometric methodology is summarized. The model properties, within sample simulations, and forecast evaluations are pre- sented. We also address methodology and practical issues relating to building and maintaining a macro model of this type. The detailed econometric equations are reported in an appendix. “I think it should be generally agreed that a model that does not gen- erate many properties of actual data cannot be claimed to have any ‘policy implications’...” Clive.W. J. Granger (1992, p. 4). 1 Introduction MOSES is a small aggregate econometric model for Sweden. The model is actively used by the Swedish Riksbank, both for policy analysis and short-term forecasting. This paper first gives a presentation of qualitative model properties, with the aid of graphics and references to macroeconomic theory. The theory behind some key aspects of the model are then discussed in more detail, before the econometric methodology used in the specification of the model is summarized. A presentation of the model properties follows in the form of simulations. Forecasts from the model for the period 2010(1)-2013(4) are presented together with outcomes for 2010(1)-2010(3). Finally, a forecast comparison with two other models in use by the Riksbank is conducted. The results of the econometric modelling are reported in detail in an Appendix. 2 Qualitative properties of MOSES MOSES represents several of the most important functional relationships in the Swedish macro economy in a small, data- and theory-coherent model. This is done by econometric We are grateful to Ulf Söderström for very helpful and detailed comments on an earlier version. Gunnar Bårdsen and Ragnar Nymoen worked as consultants for the Riksbank on this project. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Executive Board of Sveriges Riksbank. yNTNU Norwegian University of Science and Technology, Trondheim. E-mail: [email protected] zSveriges Riksbank, Monetary Policy Department, SE-103 37 Stockholm, Sweden. E-mail: [email protected] xSveriges Riksbank, Monetary Policy Department, SE-103 37 Stockholm, Sweden. E-mail: [email protected] ¶University of Oslo, Department of Economics. E-mail: [email protected] 1 modelling of aggregate product demand, interest rate setting, credit growth, the market foreign exchange and wage and price setting equations. Although MOSES is a short-term model, the concept of steady state nevertheless plays an important role in the shaping of the model’s dynamic properties. MOSES is a highly restricted dynamic Simultaneous Equations Model (SEM) with a high degree of endogeneity. Proof of this endogeneity is that both public expenditure (a fiscal policy variable) and a number of foreign variables (GDP, prices, and interest rate) are modelled as endogenous variables. This is done in order to generate MOSES forecasts that are for all practical purposes automatically generated from given initial conditions (after the model has been estimated), which can then be compared with the results of other forecasting methods and models that are part of the forecast generating systems of a major forecasting institution like the Riksbank of Sweden. The model builds on the relevant theory for each market in order to achieve the best representation. The model is also based on structural and institutional characteristics of the Swedish economy, as opposed to more stylized theory-based models. Figure1 presents the main functional relationships in MOSES in a flow chart. The line with a single arrowhead show one-way causation and joint-causation is represented by lines with arrowheads at both ends. MOSES is a model where almost all variables are endogenous. As seen in the flow chart, only the oil price (SP OIL), the electricity price (PE), the degree of accommodative labour market policy (captured by the labour market accommodation rate (AMUN), and the replacement rate (RP R)), are non-modelled variables. Foreign interest World oil price + F oreign pric es + rates (SPOIL) (PCF and PPI) (RSF and RTYF) + • • House prices Import price Exchange rate Foreign GDP (PH) (PM) + (NEX) (YF) + + /• + • + + Housing stock Electricity price Wage and price • (PE) + spiral + (HS) (P and W) • Domestic interest + rates GDP +/• (RS, RTY and RL) • (Y) • + • Unemployment (U) + +/• Real credit (CRN/P) Labour m ark et • + programmes and replacement rate Productivity Public expenditure (AMUN and RPR) (PR) (G) Exogenous Endogenous variable variable Figure 1: A flow chart of MOSES. The upper part of the chart contains relationships for the “foreign sector”. In the model, all these variables are caused by world oil prices. For example, higher energy prices leads to higher prices on foreign manufactures (PPI) and also to higher foreign 2 consumer prices (PCF ). These increases feed into the domestic wage-price spiral via the equation for import prices (PM). But the higher foreign prices (PCF ) also affect foreign GDP (YF ) in the short run, through their effect on foreign real interest rates (the money market rate (RSF ) and the 10 year bond yield rate (RT Y F )). As we have implemented the Taylor principle in foreign interest rate setting, an increase in foreign inflation leads to higher foreign real interest rates and a reduction in the growth rate of foreign GDP. Increases in foreign prices, ceteris paribus, also lead to an appreciation of the nominal exchange rate, meaning that the pass-through of foreign prices on import prices and there- fore on domestic wage and price setting is lowered through exchange rate adjustments. The supply side with the wage-price relationships (W and P ) are strongly conditioned by import prices, since Sweden is a small open economy. If domestic inflation increases, domestic interest rates will adjust upwards, first the “repo-rate” (RS), then the bond yield rate (RT Y ) and the interest rate on bank loans (RL). Because of the Taylor principle, the corresponding domestic real interest rates increases lead to reduced aggregate demand and GDP (Y ). Note however, that because of flexible inflation targeting, there is joint causation between GDP and domestic interest rates in the medium-run time perspective (this is also marked by a +/- on the connector between interest rates and GDP. We have also marked a direct (and negative) influence from domestic inflation on GDP, and this occurs through the real exchange rate. Real GDP is of course an important variable in the model. In addition to the real exchange rate and real interest rate, it is strongly conditioned by income abroad (YF ), and public expenditure (G). Domestic GDP is also influenced by the growth of real credit (CRN/P ), and in turn affects firms’and households’willingness to take on higher interest rates payments as a result of higher debt. Hence, there is a credit accelerator in the model. GDP growth is also important the evolution of the rate of unemployment (U), through an Okun’slaw relationship. Labour productivity (PR) in the model provides the link between the different labour market channels and therefore also sums up the supply-side development, normally follow- ing the same positive trend as real wages, but also positively affected by the unemployment rate, in accordance with effi ciency wage theories. 2.1 A simplified analytical exposition MOSES covers a large number of markets, and the relevant dynamic relationships between these markets. MOSES is therefore a dynamic model of some complexity. Not counting the identities, MOSES has 20 equations. However, the core of MOSES is easily interpreted in line with most standard macro theories. For example, consider making the following standard theoretical simplifying assumptions: a closed economy, no public sector, a single interest rate, no debt, no housing market, no energy, no unemployment, productivity follows a stochastic trend, and first-order dynamics. Then the qualitative properties of MOSES can be represented by the following model: pt = a12yt c11 [p (w pr) 1]t 1 (1) yt = c22 [y + 23 (R p) 2]t 1 (2) Rt = c33 Rt 1 a31 pt p a32 yt y 3 (3) (w p pr)t = c44 (w p pr + 1)t 1 (4) prt = 5 (5) where in (1) inflation pt is caused by demand effects, represented by the growth rate of 1 real output yt, and real marginal labour costs (w p pr). The dynamics of real aggre- 1 Throughout the paper lower case letters denote natural logarithms of variables, so xt ln Xt and Xt Xt 1 xt . t Xt 1 3 gate demand y in (2) is driven by the real interest rate (R p), with 2 representing the average growth rate of real output. The interest rate Rin (3) is set according to a Taylor rule, reacting to inflation deviating from its target pt p , but specified in terms of output growth deviations from target y y rather than potential output– t which is not observable. The parameter represents the natural rate of interest. The 3 wage equation (4) is simply a stationary wage share, so c44 < 1, and 1 is the log of the long-run wage share. The model is closed by assumingj thatj labour productivity follows a random walk with drift 5 in (5). To appreciate the simplifications made for ease of exposition, the MOSES econometric equivalents are given as equations (53), (54), (55), (57) and (64), respectively in the Appendix. Although simple, this standard theory model retains the qualitative aspects of MOSES. We will therefore refer to this theory-model representation when illustrating aspects of the model development below.